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020 _a9783319508061
_9978-3-319-50806-1
024 7 _a10.1007/978-3-319-50806-1
_2doi
040 _cCUS
050 4 _aQH323.5
050 4 _aQH324.2-324.25
072 7 _aPDE
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPDE
_2thema
082 0 4 _a570.285
_223
100 1 _aKiss, István Z.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematics of Epidemics on Networks
_h[electronic resource] :
_bFrom Exact to Approximate Models /
_cby István Z. Kiss, Joel C. Miller, Péter L. Simon.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXVIII, 413 p. 130 illus., 89 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v46
505 0 _aPreface -- Introduction to Networks and Diseases -- Exact Propagation Models: Top Down -- Exact Propagation Models: Bottom-Up -- Mean-Field Approximations for Heterogeneous Networks -- Percolation-Based Approaches for Disease Modelling -- Hierarchies of SIR Models -- Dynamic and Adaptive Networks -- Non-Markovian Epidemics -- PDE Limits for Large Networks -- Disease Spread in Networks with Large-scale structure -- Appendix: Stochastic Simulation -- Index.
520 _aThis textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve the differential equation models or directly simulate epidemics in networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and biology departments alike. .
650 0 _aBiomathematics.
650 0 _aDynamics.
650 0 _aErgodic theory.
650 0 _aPhysics.
650 0 _aEpidemiology.
650 0 _aProbabilities.
650 1 4 _aMathematical and Computational Biology.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M31000
650 2 4 _aDynamical Systems and Ergodic Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
650 2 4 _aApplications of Graph Theory and Complex Networks.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P33010
650 2 4 _aEpidemiology.
_0https://scigraph.springernature.com/ontologies/product-market-codes/H63000
650 2 4 _aProbability Theory and Stochastic Processes.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M27004
700 1 _aMiller, Joel C.
700 1 _aSimon, Péter L.
830 0 _aInterdisciplinary Applied Mathematics,
_x0939-6047 ;
_v46
856 4 0 _uhttps://doi.org/10.1007/978-3-319-50806-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
942 _cEBK
999 _c207108
_d207108